From the top of a tall building, a gun is fired. The bullet leaves the gun at a speed of 340 m/s, parallel to the ground. As the drawing shows, the bullet puts a hole in a window of another building and hits the wall that faces the window. (y = 0.44 m, and x = 6.8 m.) Using the data in the drawing, determine the distances D and H, which locate the point where the gun was fired. Assume that the bullet does not slow down as it passes through the window. D is the distance between the buildings and H is the height the bullet falls to reach the window.

Question

From the top of a tall building, a gun is fired. The bullet leaves the gun at a speed of 340 m/s, parallel to the ground. As the drawing shows, the bullet puts a hole in a window of another building and hits the wall that faces the window. (y = 0.44 m, and x = 6.8 m.) Using the data in the drawing, determine the distances D and H, which locate the point where the gun was fired. Assume that the bullet does not slow down as it passes through the window. D is the distance between the buildings and H is the height the bullet falls to reach the window.

Answer 1

Also, y is the height of the hole in the window and x is the distance from the front of the building to the bullet.

Answer 2

To find the distances D and H, we can use the kinematic equations of motion. Here's how we can approach the problem:

1. Determine the time it takes for the bullet to travel the horizontal distance, D:
We know that the horizontal component of the bullet's velocity is constant because there is no acceleration in that direction. Therefore, we can use the equation:
D = Vx * t (Equation 1)
Here, Vx represents the horizontal component of the bullet's velocity, which is given as 340 m/s.

2. Determine the time it takes for the bullet to fall to the window, H:
The vertical motion of the bullet is influenced by gravity and can be calculated using the equation:
H = (1/2) * g * t^2 (Equation 2)
Here, g represents the acceleration due to gravity, which is approximately 9.8 m/s^2.

3. Find the total time taken by the bullet:
Since the bullet simultaneously travels horizontally and vertically, the total time taken can be determined by equating the time in both equations. Solving for t in Equation 1 and substituting into Equation 2, we get:
H = (1/2) * g * (D/Vx) ^ 2 (Equation 3)

4. Calculate the distances D and H:
Substitute the given values into Equation 3 to find D and H:
H = (1/2) * 9.8 * (D/340) ^ 2
Now, plug in the given values of H = 0.44 m and D = 6.8 m to solve for the unknowns.

By solving the equation, you will find the values of D and H, which locate the point where the gun was fired.